The present invention relates to a method for damping power oscillations in transmission lines, and to a device for carrying out the method.
The device comprises means for forming a damping signal in dependence on the amplitude of an estimated power quantity and with an eligible phase shift in relation to the phase position thereof, and an actuator to be influenced in dependence on the damping signal and hence to influence the power transmitted in the transmission line
In transmission lines, which connect two separate power networks or which connect two parts in one and the same power network, a constant phase-angle difference is maintained, during steady state at a certain transmitted power, between the voltages at the end points of the transmission line. Each change of the transmitted power entails a change of this angular difference. Because of the moments of inertia of the generators in the power network(s), each such change of the angular difference occurs in an oscillating manner with natural frequencies typically in the interval of 0.1 to 2 Hz. The internal damping of these power oscillations is often very small, and, in addition, decreases with increasing amplitude of the oscillation. If the amplitude of the oscillation is sufficiently great, the internal damping may even become negative, in which case the oscillation amplitude grows in an uncontrolled manner such that the transmission of power via the transmission line has to be interrupted.
Especially great power oscillations may occur upon a rapid disconnection of generators or in connection with lines in the power system being disconnected, for example in connection with short circuits on the transmission line or in some of the connected power systems.
FIG. 1 shows a typical appearance of a disturbance in the active power in a transmission line included in a power system, for example in case of a loss of a generator which is connected to and feeds power into the power system. The time t is plotted on the horizontal axis and the instantaneous active power p(t) is plotted on the vertical axis. In a given time interval, the disturbance may be characterized by a mean power Pav and an oscillating component xcex94p(t), the latter having an angular frequency xcexa9=2xcfx80f. As mentioned above, the frequency f usually lies within the interval 0.1 to 2 Hz.
The damping of the power oscillations may be improved by influencing the power transmitted by the transmission line. In a known way, this influence may, for example, be achieved:
by influencing the terminal voltage of a generator connected to the power network(s) by means of a so-called Power System Stabilizer (PSS), which influences the magnetization equipment for the generator and hence the terminal voltage thereof,
by influencing the total reactance of the transmission line by means of a controllable series capacitor connected into the line, a so-called Thyristor Controlled Series Capacitor (TCSC), in which case thus the total reactance of the transmission line consists of the line reactance plus the reactance of the series capacitor, or
by supplying/consuming reactive power at some point on the transmission line by means of a so-called reactive-power compensator (Static Var Compensator, SVC), which influences the voltage at that point on the fine where the compensator is connected and hence also the power flow in the transmission line.
The generator, the controllable series capacitor, and the reactive-power compensator, respectively, constitute actuators which modulate each of the above-mentioned quantities, the terminal voltage of the generator, the total reactance of the transmission line, the voltage at a certain point along the line, such that, in addition to the original power oscillation, an additional controlled power variation is achieved. If this controlled power variation is carried out with the same frequency as the original oscillation and with a phase position which deviates 90xc2x0 from the phase position thereof, a damping of the original oscillation is obtained.
In order not to burden the representation with distinctions which are self-explanatory to the person skilled in the art, in the following description the same designations are generally used for quantities which occur in the installation as for the measured values and signals/calculating values, corresponding to these quantities, which are supplied to and processed in the control equipment which will be described in the following.
FIG. 2 schematically shows a known embodiment of damping equipment by means of a Power System Stabilizer (PSS). A generator 1 is connected, via a power transformer T1, to a transmission line 2, which in turn is connected to a power network N2 with an additional line 3 (only roughly indicated). The generator has magnetization equipment 1a. The voltage V and the current I through the transmission line are sensed by means of a voltage transformer T2 and a current-measuring device IM, respectively. A voltage controller 4, only symbolically shown, is supplied with a voltage-reference signal VREF and a measured value VSVAR of the actual value of the voltage V, which measured value is obtained via the voltage transformer T2. The output signal from the voltage controller is supplied to the magnetization equipment of the generator and influences its excitation current in such a way that the measured value VSVAR approaches the voltage-reference signal VREF to correspond thereto at least under steady-state conditions.
A power-calculating member 5 is supplied with the measured value VSVAR and with a measured value i(t) of the actual value of the current I and calculates therefrom a calculating value p(t) of the active power delivered to the power network N2 by the generator. This calculating value is supplied to an identification member 6 for identification of the amplitude and the phase position of a power oscillation, if any. The identification member forms from the calculating value p(t) a control signal xcex94VPSS which is supplied to the voltage controller of the generator as an addition in addition to the normal voltage reference VREF. Since the power oscillation in the transmission line also occurs in the power delivered by the generator, in this way also a damping of the power oscillation in the transmission line may be achieved.
A known embodiment of the identification member 6 is illustrated in FIG. 4. The calculating value p(t) is supplied to a so-called washout filter 61 with a transfer function             sT      w              1      +              sT        w              ,
where s is the Laplace operator. The filter separates the constant or slowly varying component Pav of the calculating value p(t) but forwards the oscillating part thereof. The filter has a cutoff frequency   1      2    ⁢          xe2x80x83        ⁢    π    ⁢          xe2x80x83        ⁢          T      w      
chosen with a sufficient distance from the frequency of the oscillation which is to be damped.
The above-mentioned desired phase shift of 90xc2x0 of the oscillating part of the calculating value p(t) is achieved with the aid of one or more lead-lag filters, in this embodiment by means of two cascade-connected filters 62 and 63 with the transfer functions       1    +          sT      1            1    +          sT      2      
and             1      +              sT        3                    1      +              sT        4              ,
respectively.
The output signal D(t) from the lead-lag filter 63 constitutes a damping signal which, after a necessary adaptation (not shown in the figure) of the signal level to constitute the control signal xcex94VPSS, is utilized for modulating the terminal voltage of the generator, thus achieving the desired controlled power variation.
Because of limitations of the available control range of the actuators (limited by the maximum stresses which the apparatus may endure), limitations (only roughly indicated in the figure) of the output signals from the lead-lag filters are introduced.
These limitations have an adverse effect on the efficiency of the damping equipment in that the effective amplification at large signals is reduced below the nominal amplification at small oscillating amplitudes when the limitations are not active.
Experience shows that, in case of disturbances of the power systems, a change of the mean power on the transmission line is obtained, almost without exception, at the same time as the oscillation is initiated. This is illustrated in FIG. 1 which also shows how the original power is slowly stabilized at a new level. This return is controlled by overriding control systems in the power system and has a negligible effect on the power oscillation. However, a further problem is that the fast change of the mean power which occurs when a power oscillation starts (see FIG. 1) causes an undesired transient contribution to the output signal from the washout filter. This contribution tends to make the total output signal from the filter so large as to exceed the available control range of the actuators. To counteract this, limitations in the lead-lag filters, according to some so-called non-integral windup strategy, are introduced. A negative consequence of this process, however, is that the maintenance of the desired phase shift in the lead-lag filters is rendered difficult.
In a power system with more than two generators, several oscillation modes with different frequencies occur, in which different groups of generators oscillate between themselves. This causes damping equipment, the control equipment of which is based on the prior art according to FIG. 4, to react on the different oscillation modes, a consequence of which may be that oscillation modes, which per se have an acceptable internal damping, may be disturbed by action from the damping equipment.
FIG. 3 schematically shows a known embodiment of damping equipment in which the actuator is in the form of a controllable series capacitor (TCSC) A generator G1 is connected, via a power transformer T1, to a power network N1, and a generator G2 is connected, via a power transformer T3, to a power network N2. The power networks are interconnected by means of at least one transmission line 2, into which a controllable series capacitor 7 is connected. It is assumed in the following that the controllable series capacitor, in a manner known per se, is controlled by a reactance regulator 8 via a reference value XREF for its reactance.
A power-calculating member 5 calculates, in a manner similar to that described with reference to FIG. 2, a calculating value p(t) of the active power transmitted by the transmission line. The calculating value is supplied to a reactance calculating member 9 which comprises washout and lead-lag filters, as described with reference to FIG. 4, as well as an adaptation (not shown in the figure) of the damping signal D(t) to constitute a correction value xcex94XPOD. This correction value is supplied, together with the reference value XREF for the reactance of the series capacitor, to a summing member 10, the output signal of which is supplied to the reactance regulator 8 to achieve the desired controlled power variation.
FIG. 9A schematically shows a known embodiment of damping equipment in which the actuator is in the form of a reactive-power compensator (SVC), and in which corresponding parts of the figure, and, where applicable, corresponding quantities, have been given the same reference numerals as in FIG. 3. A reactive-power compensator 7xe2x80x2 is connected in shunt connection to the transmission line 2 at a connection point J1. The impedance of the transmission line between the connection point and the power networks N1 and N2 are marked in the figure as line reactances LR1 and LR2, respectively. The compensator is adapted, in a manner known per se, to influence the voltage V at the connection point J1 via a voltage regulator 8xe2x80x2 which, as output signal, forms and supplies to the compensator a reference value B(t) for its susceptance.
A difference-forming member 4xe2x80x2 is supplied and forms as output signal the difference of a voltage-reference value VREF and a measured value VSVAR obtained via the voltage transformer T2, of the actual value of the voltage V, which output signal is supplied to the voltage controller.
The calculating value p(t) is supplied to a calculating member 9xe2x80x2 which comprises washout and lead-lag filters as described with reference to FIG. 4, and an adaptation (not shown in the figure) of the damping signal D(t) to constitute a correction value xcex94U(t). This correction value is supplied to the difference-forming member 4xe2x80x2 as an addition to the voltage-reference value VREF. The reference value B(t) for the susceptance of the compensator is thus formed in dependence on the correction value xcex94U(t).
When the voltage at the connection point J1 varies (in dependence on the correction value xcex94B(t)), also the active power flow in the transmission line will be influenced. It is to be noted that the relation between the voltage variation and the power variation depends on the location of the compensator along the transmission line as well as on the voltage characteristic for the load placed at the receiving end of the line, in the figure marked as a load L connected to the power network N2. An increase of the voltage at the connection point J1 usually leads to an increase of the transmitted active power, which relieves the generator G2. In the event that the compensator (in this example) is connected near the power network N2 and, in addition, the load L is of a certain magnitude and/or is greatly dependent on the voltage, it may, however, happen that a voltage increase at the connection point J1 leads to such a large power increase in the load L that the load on the generator G2 instead increases. Under these circumstances, a reversal of the signs of correction values xcex94U(t) to the reference value of the voltage controller must thus take place in order for a correct damping of the power oscillations to be obtained.
The object of the invention is to achieve a method of the kind described in the introduction, which permits a fast and robust identification of a component of the power oscillation, oscillating with a given angular frequency, without the identification being disturbed by the simultaneously occurring change of the mean power and of oscillations with deviating angular frequencies, and to a device for carrying out the method.
According to the invention, this is achieved by generating at least one first angular-frequency signal, representing a first angular frequency which is given by a priori knowledge of oscillation frequencies expected in the power system, forming a first phase-reference signal as the time integral of the first angular-frequency signal, sensing a power quantity characterizing for the power transmitted by the transmission line, forming a first estimated power quantity in dependence on the characterizing power quantity, representing for an oscillation of the first angular frequency its amplitude and phase position relative to the first phase-reference signal, forming a first damping signal with an amplitude in dependence on the amplitude of the first estimated power quantity and with an eligible first phase shift in relation to the phase position thereof, and by influencing an actuator in dependence on the first damping signal to thereby influence the power transmitted in the transmission line.
In an advantageous development of the invention, whereby the power system exhibits at least two oscillation modes, at least one second angular-frequency signal is generated in addition thereto, representing a second angular frequency which is given by a priori knowledge of oscillation frequencies expected in the power system, a second phase-reference signal is formed as the time integral of the second angular-frequency signal, a second estimated power quantity is formed in dependence on the characterizing power quantity, representing for an oscillation of the second angular frequency its amplitude and phase position relative to the second phase-reference signal, a second damping signal is formed with an amplitude in dependence on the amplitude of the second estimated power quantity and with an eligible second phase shift in relation to the phase position thereof, and the actuator is influenced also in dependence on the second damping signal.
In another advantageous development of the invention, a correction frequency to the angular-frequency signal(s) is formed in dependence on the actual frequency of the power oscillations when the amplitude of the oscillating component in the estimated power quantity/quantities exceeds an eligible level.
In a further advantageous development of the invention, the damping signal(s) is/are deactivated if the correction frequency exceeds or falls below the respective given levels.
In still another advantageous development of the invention, the amplitude of the damping signal(s) is formed in dependence on an amplification factor which increases with increasing amplitude of the respective estimated power quantity/quantities mentioned.
In yet another advantageous development of the invention, the eligible phase shift(s) mentioned is/are formed in dependence on the amplitude of an estimated value of the mean power in the transmission line.
Further advantageous developments and embodiments of the invention will become clear from the following description and the appended claims.